Exponential Krylov peer integrators

This paper is concerned with the application of exponential peer methods to stiff ODEs of high dimension. Conditions for stiff order p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document} for variable step size are derived, and corresponding methods are given. The methods are combined with Krylov approximations for the φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi $$\end{document}-functions times a vector using the code phipm of Niesen and Wright. The structure of the peer methods is exploited to reduce the Krylov dimensions. Numerical tests with step size control of three exponential peer methods and comparisons with the exponential W-method exp4 for semidiscretized problems show the efficiency of the proposed methods.